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Eulerian Graphs

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Let G be a graph. The line graph L(G) of G is defined to be the graph whose vertices are the edges of G and where two vertices of L(G) are adjacent if the corresponding edges of G are adjacent. Prove that if G is connected, then L(G) is eulerian if vertices of G are all odd or all even.

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Solution Summary

Eulerian graphs are investigated. The solution is detailed and well presented.

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It should be in your textbook but just in case here is a web reference - http://en.wikipedia.org/wiki/Eulerian_path - containing the definition of Eulerian graphs and statement saying that Eulerian graphs are connected, undirected, and their vertices are all of even degree.

Observation A:
Let n_i denote ...

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